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st: aweight option in kdensity
Dear all,
I have problem understanding the aweight option
in kdensity command and the manual (and everywhere
else I have read) is not helping. Please help?
Also, please correct me if my understanding is wrong.
Basically, if I have a survey data of people's income
in a country. Let's say I have n observation in
my data and each observation has its own weight
(sampling weight -- I believe it's called probability
weight in stata?). These weights will sum to the country's
population. This weight variable is named MY_w.
(sum of MY_w over all the n observations equals to the
country's population)
Now, I want to estimate the density of their income.
--------------------
if I do:
kdensity income
Then, I don't take into account of those sampling
weights. The formula is:
[equation 1]
f(x) = {1/nh} {sigma[(K(x - xi)/h)]}
h--bandwidth
n--sample size
K--kernal function
xi--each observation's income
sigma--summation i = 1 to n
So I assume that each observation is sampled at equal
probability of 1/n -- which is wrong?
--------------------
I think the weight I have is pweight but kdensity
doesn't allow pweight. It only allows fweight and
aweight. It seems like fweight is out of the question.
I should be doing this?
[equation 2]
f(x) = {1/h} {sigma [wi * K((x - xi)/h)]}
where wi is the probability of that observation being
sampled (so wi was 1/n in [equation 1])
Now, I wonder if kdensity with aweight can give me
the estimate of [equation 2]
Should I be doing this?
kdensity income [aw=MY_W]
or should I be doing this?
kdensity income [aw=1/MY_W]
or I shouldn't use aweight and try to edit the command
by my owen? Would the unweighted version be wrong?
Thank you very much.
Best regards,
Vora N
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